Mixing forward and inverse kinematics
There is no built-in way to perform that task.

Many rigs provide python scripts that show panels in the 3dview for controls such as layer display and IK/FK switching, many also include scripts that snap IK bones to the position of FK bones and vice versa.

You can find the rigify scripts that are included with blender within the addons folder where you can look at how this can be achieved.

Most animators will tend to use one or the other depending on the actions being animated, keying the IK/FK influences on a transition frame when they change over. I believe you will find it difficult to be using both on every frame and only create extra work for yourself.